Nuprl Lemma : alle-lt-iff
∀es:EO. ∀e':E.
∀[P:{e:E| loc(e) = loc(e') ∈ Id} ⟶ ℙ]. (∀e<e'.P[e] ⇐⇒ P[pred(e')] ∧ ∀e<pred(e').P[e] supposing ¬↑first(e'))
Proof
Definitions occuring in Statement :
alle-lt: ∀e<e'.P[e],
es-first: first(e),
es-pred: pred(e),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
and: P ∧ Q,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
alle-lt: ∀e<e'.P[e],
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
uimplies: b supposing a,
member: t ∈ T,
not: ¬A,
false: False,
prop: ℙ,
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s],
es-locl: (e <loc e'),
subtype_rel: A ⊆r B,
rev_implies: P ⇐ Q,
es-E: E,
es-base-E: es-base-E(es),
or: P ∨ Q
Latex:
\mforall{}es:EO. \mforall{}e':E.
\mforall{}[P:\{e:E| loc(e) = loc(e')\} {}\mrightarrow{} \mBbbP{}]
(\mforall{}e<e'.P[e] \mLeftarrow{}{}\mRightarrow{} P[pred(e')] \mwedge{} \mforall{}e<pred(e').P[e] supposing \mneg{}\muparrow{}first(e'))
Date html generated:
2016_05_16-AM-09_42_15
Last ObjectModification:
2015_12_28-PM-09_41_39
Theory : new!event-ordering
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