Nuprl Lemma : FormEqual_wf2
∀[C:Type]. ∀[a,b:PZF-Term(C)]. (a = b ∈ PZF-Formula(C))
Proof
Definitions occuring in Statement :
PZF-Formula: PZF-Formula(C),
PZF-Term: PZF-Term(C),
FormEqual: left = right,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
PZF-Term: PZF-Term(C),
PZF-Form: PZF-Form(C),
PZF-Formula: PZF-Formula(C),
and: P ∧ Q,
cand: A c∧ B,
prop: ℙ,
not: ¬A,
implies: P ⇒ Q,
false: False,
assert: ↑b,
ifthenelse: if b then t else f fi ,
termForm: termForm(f),
Form_ind: Form_ind,
FormEqual: left = right,
bfalse: ff,
wfForm: wfForm(f),
wfFormAux: wfFormAux(f),
bnot: ¬bb,
band: p ∧b q,
btrue: tt,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
uimplies: b supposing a,
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
true: True,
SafeForm: SafeForm(f)
Lemmas referenced :
FormEqual_wf,
assert_wf,
wfForm_wf,
SafeForm_wf,
termForm_wf,
not_wf,
PZF-Term_wf,
assert_of_band,
wfFormAux_wf,
btrue_wf,
squash_wf,
true_wf,
bool_wf,
iff_imp_equal_bool
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
productElimination,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
hypothesis,
independent_pairFormation,
productEquality,
lambdaFormation,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality,
applyEquality,
independent_isectElimination,
hyp_replacement,
lambdaEquality,
imageElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[C:Type]. \mforall{}[a,b:PZF-Term(C)]. (a = b \mmember{} PZF-Formula(C))
Date html generated:
2018_05_21-PM-11_37_45
Last ObjectModification:
2017_10_12-PM-05_10_43
Theory : PZF
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