Nuprl Lemma : weak-antecedent-function-property
∀[es:EO]. ∀[P,Q:E ⟶ ℙ]. ∀[f:{e:E| P e} ⟶ E]. f ∈ {e:E| P e} ⟶ {e:E| Q e} supposing Q ←==f== P
Proof
Definitions occuring in Statement :
weak-antecedent-function: Q ←==f== P,
es-E: E,
event_ordering: EO,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
weak-antecedent-function: Q ←==f== P,
prop: ℙ,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
and: P ∧ Q
Latex:
\mforall{}[es:EO]. \mforall{}[P,Q:E {}\mrightarrow{} \mBbbP{}]. \mforall{}[f:\{e:E| P e\} {}\mrightarrow{} E]. f \mmember{} \{e:E| P e\} {}\mrightarrow{} \{e:E| Q e\} supposing Q \mleftarrow{}==f== P
Date html generated:
2016_05_16-AM-10_16_02
Last ObjectModification:
2015_12_28-PM-09_23_48
Theory : new!event-ordering
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