Nuprl Lemma : qeq-refl
Refl(ℤ ⋃ (ℤ × ℤ-o);r,s.qeq(r;s) = tt)
Proof
Definitions occuring in Statement :
qeq: qeq(r;s),
refl: Refl(T;x,y.E[x; y]),
int_nzero: ℤ-o,
b-union: A ⋃ B,
btrue: tt,
bool: 𝔹,
product: x:A × B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
refl: Refl(T;x,y.E[x; y]),
all: ∀x:A. B[x],
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
bool_wf,
qeq_refl,
btrue_wf,
iff_weakening_equal,
b-union_wf,
int_nzero_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeEquality,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination,
because_Cache,
intEquality,
productEquality
Latex:
Refl(\mBbbZ{} \mcup{} (\mBbbZ{} \mtimes{} \mBbbZ{}\msupminus{}\msupzero{});r,s.qeq(r;s) = tt)
Date html generated:
2018_05_21-PM-11_43_41
Last ObjectModification:
2017_07_26-PM-06_42_55
Theory : rationals
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