Nuprl Lemma : eu-eq_dist-axiomsA
∀g:EuclideanPlane. dist-axiomsA(g)
Proof
Definitions occuring in Statement :
dist-axiomsA: dist-axiomsA(g),
euclidean-plane: EuclideanPlane,
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
dist-axiomsA: dist-axiomsA(g),
member: t ∈ T,
uall: ∀[x:A]. B[x],
euclidean-plane: EuclideanPlane,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
false: False,
so_apply: x[s],
so_lambda: λ2x.t[x],
cand: A c∧ B,
exists: ∃x:A. B[x],
dist: D(a;b;c;d;e;f),
uiff: uiff(P;Q),
basic-geometry: BasicGeometry,
or: P ∨ Q,
stable: Stable{P},
geo-eq: a ≡ b,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
sq_stable: SqStable(P),
squash: ↓T,
true: True,
pi2: snd(t),
geo-seg2: geo-seg2(s),
geo-mk-seg: ab,
pi1: fst(t),
geo-seg1: geo-seg1(s),
geo-seg-congruent: geo-seg-congruent(e; s1; s2),
geo-lt: p < q,
basic-geometry-: BasicGeometry-,
geo-strict-between: a-b-c,
sq_exists: ∃x:A [B[x]],
geo-colinear-set: geo-colinear-set(e; L),
l_all: (∀x∈L.P[x]),
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
select: L[n],
cons: [a / b],
subtract: n - m,
oriented-plane: OrientedPlane,
geo-lsep: a # bc,
top: Top,
le: A ≤ B,
less_than': less_than'(a;b),
less_than: a < b,
append: as @ bs,
so_lambda: so_lambda3,
so_apply: x[s1;s2;s3]
Latex:
\mforall{}g:EuclideanPlane. dist-axiomsA(g)
Date html generated:
2020_05_20-AM-10_50_29
Last ObjectModification:
2020_01_13-PM-09_42_56
Theory : euclidean!plane!geometry
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