Nuprl Lemma : r2-line-eq_weakening
∀l,m:r2-line. ((l = m ∈ r2-line) ⇒ r2-line-eq(l;m))
Proof
Definitions occuring in Statement :
r2-line-eq: r2-line-eq(l;m),
r2-line: r2-line,
all: ∀x:A. B[x],
implies: P ⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x],
not: ¬A,
r2-line-eq: r2-line-eq(l;m),
and: P ∧ Q,
exists: ∃x:A. B[x],
r2-line-sep: r2-line-sep(l;m),
iff: P ⇐⇒ Q,
pi2: snd(t),
pi1: fst(t),
r2-line: r2-line,
req: x = y,
rev_implies: P ⇐ Q,
nat_plus: ℕ+,
le: A ≤ B,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top
Lemmas referenced :
r2-line_wf,
equal_wf,
r2-line-eq_wf,
r2-line-sep_wf,
int-to-real_wf,
r2-det_wf,
rneq-iff,
nat_plus_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermVar_wf,
itermConstant_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf
Rules used in proof :
hypothesisEquality,
hypothesis,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
dependent_functionElimination,
applyLambdaEquality,
equalitySymmetry,
hyp_replacement,
productElimination,
independent_functionElimination,
natural_numberEquality,
sqequalRule,
setElimination,
rename,
independent_isectElimination,
approximateComputation,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation
Latex:
\mforall{}l,m:r2-line. ((l = m) {}\mRightarrow{} r2-line-eq(l;m))
Date html generated:
2019_10_30-AM-11_32_39
Last ObjectModification:
2018_09_06-PM-03_06_06
Theory : reals!model!euclidean!geometry
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