Nuprl Lemma : weak-antecedent-function_functionality_wrt_pred_equiv
∀es:EO. ∀[P,Q,P',Q':E ─→ ℙ]. ∀f:{e:E| P e} ─→ {e:E| Q e} . (P ⇐⇒ P' ⇒ Q ⇐⇒ Q' ⇒ (Q ←==f== P ⇐⇒ Q' ←==f== P'))
Proof
Definitions occuring in Statement :
weak-antecedent-function: Q ←==f== P,
es-E: E,
event_ordering: EO,
predicate_equivalent: P1 ⇐⇒ P2,
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ─→ B[x]
Lemmas :
subtype_rel_sets,
set_wf,
es-E_wf
\mforall{}es:EO
\mforall{}[P,Q,P',Q':E {}\mrightarrow{} \mBbbP{}].
\mforall{}f:\{e:E| P e\} {}\mrightarrow{} \{e:E| Q e\} . (P \mLeftarrow{}{}\mRightarrow{} P' {}\mRightarrow{} Q \mLeftarrow{}{}\mRightarrow{} Q' {}\mRightarrow{} (Q \mleftarrow{}==f== P \mLeftarrow{}{}\mRightarrow{} Q' \mleftarrow{}==f== P'))
Date html generated:
2015_07_17-AM-09_01_55
Last ObjectModification:
2015_01_27-PM-00_55_50
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