Nuprl Lemma : eq_int_eq_false_intro
∀[i,j:ℤ]. (i =z j) ~ ff supposing ¬(i = j ∈ ℤ)
Proof
Definitions occuring in Statement :
eq_int: (i =z j),
bfalse: ff,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
int: ℤ,
sqequal: s ~ t,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
nequal: a ≠ b ∈ T ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
sq_type: SQType(T),
all: ∀x:A. B[x]
Lemmas referenced :
subtype_base_sq,
bool_wf,
bool_subtype_base,
equal_wf,
squash_wf,
true_wf,
eq_int_eq_false,
bfalse_wf,
subtype_rel_self,
iff_weakening_equal,
not_wf,
equal-wf-base,
int_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
hypothesis,
independent_isectElimination,
applyEquality,
lambdaEquality,
imageElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
because_Cache,
productElimination,
independent_functionElimination,
dependent_functionElimination,
axiomSqEquality,
intEquality,
isect_memberEquality
Latex:
\mforall{}[i,j:\mBbbZ{}]. (i =\msubz{} j) \msim{} ff supposing \mneg{}(i = j)
Date html generated:
2019_06_20-AM-11_33_12
Last ObjectModification:
2018_09_18-PM-02_14_46
Theory : int_1
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